# Proof of Field D*'s Case Separation for Arbitrary Simplices

Merry, Bruce, Simon James Perkins, Patrick Marais and James Gain (2012) Proof of Field D*'s Case Separation for Arbitrary Simplices. Technical Report CS12-07-00, Department of Computer Science, University of Cape Town.

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## Abstract

In their development of the Field D* algorithm, Ferguson et. al. prove that a path through a unit length right-angled triangle originating from an interpolated edge, and travelling to the opposite vertex must either be a direct or indirect case. A combination of the two is not optimal. Later work, proves this for arbitrary, but non-degenerate triangles.

In this technical report, we prove the same for non-degenerate simplices, which are generalisations of triangles to higher dimensions.

EPrint Type: | Departmental Technical Report |
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Keywords: | computational geometry mathematical proof |

Subjects: | I Computing Methodologies: I.2 ARTIFICIAL INTELLIGENCE |

ID Code: | 785 |

Deposited By: | Perkins, Simon |

Deposited On: | 25 September 2012 |